Ij pyi j Ek1 hik

xi = ith row of fixed effects design matrix X, a = vector of fixed effects parameters.

Note that there is a separate equation for each partition, j.

• Maximising the likelihood function for the model parameters (the Ij and a) based on the multinomial distribution. Methods for maximising the likelihood function coincide with those for the mixed ordinal logistic regression model and are described in Section 4.2. They are based on using the matrix notation below to represent the multinomial distribution.

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